The Flash Calculation

A flash operation occurs when a mixture is expanded through a valve from a region of relatively high pressure to a region of relatively low pressure. Because of the change in temperature and pressure, a phase separation can be induced. In this type of process, the temperature and pressure at the final state are known, and while the compositions of the equilibrium vapor and liquid phases are unknown, the composition of the fluid entering the valve is known. 

In order to solve this type of problem, we require an overall mass balance to relate the amount of vapor (V) and liquid (L) to the total amount of material (F) 

Similar equations can be written for each species in the mixture. Defining the mole fraction of the species in the vapor as y., the mole faction of the species in the liquid as X., and the mole fraction of the species in the original fluid as z., provides the species mass balance 

We incorporate the equilibrium data using the distribution coefficient (which can be obtained from Antoine s equation if necessary) 

This equation contains two unknowns, L and Xj. We would like to solve for x- and then sum over all of the species, since IX = 1. Skipping several steps of mathematics, we find 

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The calculation of y and P in Equation 14.16a is achieved by bubble point pressure-type calculations whereas that of x and y in Equation 14.16b is by isothermal-isobaric //cm-/(-type calculations. These calculations have to be performed during each iteration of the minimization procedure using the current estimates of the parameters. Given that both the bubble point and the flash calculations are iterative in nature the overall computational requirements are significant. Furthermore, convergence problems in the thermodynamic calculations could also be encountered when the parameter values are away from their optimal values. 

For flashing liquids composed of many miscible substances, the flash calculation is complicated considerably, because the more volatile components flash preferentially. Procedures are available to solve this problem.16... 

The relaxation method is certainly slower than the other methods of calculation. However, because of its simple nature, any process can be calculated and the complexities of the process cease to be a major concern. If future attention were directed toward performing an exact calculation of the individual stage, these more exact calculations could replace the flash calculations of the theoretical stages, and the calculated process would then fit much more closely the actual process operation. 

The predictions of the flash calculation show only the total amounts of vapor and liquid resulting. If a side vapor or side liquid flow has been specified from the stage it must be subtracted from the total phase, the remainder constituting the flow to the adjoining stage. This is done be-between statements 106 and 111. If it is found, for example, the predicted amount of liquid is less than the set amount of side liquid flow, all of the predicted liquid phase will be used as side flow and the flow of liquid to the stage below will be set at zero. The vapor is treated in the same way, but in either case the program notes that the problem has been altered. 

In the case of the flash calculations, different algorithms and schemes can be adopted the case of an isothermal, or PT flash will be considered. This term normally refers to any calculation of the amounts and compositions of the vapour and the liquid phase (V, L, y,-, xh respectively) making up a two-phase system in equilibrium at known T, P, and overall composition. In this case, one needs to satisfy relation for the equality of fugacities (eq. 2.3-1) and also the mass balance equations (based on 1 mole feed with N components of mole fraction z,) ... 

The results of the flash calculations are in terms of pound-moles. The molecular weights and densities of the coexisting gas and liquid also must be calculated in order to reproduce page 4 of Table 10-1. The compositions of the equilibrium gas and liquid are used to calculate these molecular weights and densities. 

V9 Specific volume of the mixture evaluated at 90% of the flowing pressure at inlet temperature, V, after a flash calculation. The flash calculation should preferably be carried out isentropically, but isenthalpic flash is sufficient m3/kg... 

One further vapor/liquid equilibrium problem is the flash calculation. origin of the name is in the change that occurs when a liquid under press passes through a valve to a pressure low enough that some of the liquid vapori or flashes, producing a two-phase stream of vapor and liquid in equilibri We consider here only the P.f -flash, which refers to any calculation of quantities and compositions of the vapor and liquid phases making up a two-ph system in equilibrium at known P, T, and overall composition. 

The flash calculation illustrated by Example 10.3 for a system obeying Raoult s law was solved by a very simple trial procedure. This was possible becau K-values (K( = yjxi) could be calculated from knowledge of T and P alone When the K-values depend not only on T and P but also on the phase compos1 tions, their calculation is inherently more difficult. Moreover, since the pha compositions are not initially known, they are most conveniently found by iterative computation scheme. 

Since the given pressure lies between Pb and Pdt we proceed to the flash calculation. 

As was pointed out earlier, molecular distillation is normally used to fractionate mixtures of components of very low volatility. It is proposed that a supercritical fractionation process, as schematically shown in figure 6, can be used to produce fractions superior to that of molecular distillation. In order to test this, a molecular distillation model must be used. As a first approximation, the molecular distillation of high molecular weight alkanes is viewed as a simple flash. The vapour pressure data of Kudchadker et al[10] was used in the flash calculations. 

The dew point and bubble point calculations do not present peculiar problems, but the flash calculation does. Let X fx) be the mole fraction distribution in the feed to a flash, and let a be the vapor phase fraction in the flashed system. The mass balance is ... 

The flash calculation is a very common application of VLE. Considered here is the P, T flash, in which are calculated the quantities and compositions of the vapor and liquid phases in equilibrium at known T, P, and overall composition. This problem is determinate on the basis of Duhem s theorem For any closed systemformed initallyfrom... 

The method described here is based on the vapor-liquid equilibrium relationships given in handbooks available from the Gas Processors Suppliers Association. This technique will handle flash calculations with feed streams containing up to 15 components. As an added feature, the calculation will check the feed composition at flash conditions for dew point or bubble point condition (i.e., whether the feed is either all vapor or all liquid). These checks are done before the flash calculations are started. If the feed is above the dew point or below the bubble point, an appropriate message is displayed on the computer screen. A default value for R (L/V) = 1.0 is used to start the iterative process. 

The flash calculations are done iteratively as described above. The sample calculations are shown here for the last (converged) pass. Liquid and vapor compositions from the previous pass are... 

For the calculation of the equilibrium phase compositions, it is convenient to use the distribution coefficient C (= x, /x p) to perform a flash calculation. The distribution coefficient for the flash calculation is now formed according to Equation (4.527) by... 

One of the most powerful aspects of the HCToolkit is its extensibility in Perl. This allows rapid development of new applications for specific tasks. For example, an included extension quickly calculates and plots a pressure-temperature phase diagram at user-specified conditions (PT-PhaseDiagram.pl, found in the /apps subdirectory of the distribution tree). In fact, a scripting application that does some sort of equilibrium calculation needs only do four things create a database connection, use that connection to load a pre-defined fluid, initialize the flash object and do the flash calculation. These steps are shown in Figure 4. 

The feed composition given in Table 2 has been used in the flash calculations with the relevant amount of nitrogen or aromatic compound in order to determine the amount of surface occupied by each poison and hence it s poisoning power. 

A2. Can weight units be used in the flash calculations instead of molar units ... 

This value for the enthalpy of vaporization obtained with Option 3 is considerably higher than the one obtained with Option 2, as the flash calculation can take the temperature rise of the liquid into account. In this case, where a wide boiling mixture is regarded, even this incremental evaporation with the 0.001 vapor fraction causes a temperature rise in the liquid by 0.06 K, which has a considerable influence on the calculated heat of vaporization. For illustration, the mass balance is listed in Table 6.1 In fact, this example is an extreme one due to the wide boiling range. Usually, Option 2 should yield a better approximation and could be used for a rough check. Nevertheless, as there is no way to avoid the flash... 

A dynamic model for the Flash separator in the plant has been developed. A two-phase mixture is formulated in the flash tank, a polymer-rich (Heavy) and a polymer-lean (Light) gas phase. Thermodynamic equilibrium is assumed to settle instantaneously between the phases and the flash calculations are carried out employing the S-L EoS. It... 

For some mixtures, if the BWR-11 or BWR-8 equation is used in the flash calculation, the bubble-point at C can be obtained. However, in some case studies, if the Initial temperature guess was D, the bubble-point at B would be obtained rather than C. In these cases, going one step further, even if the initial temperature guess was temperature C the program would converge on bubble-point B. This could be a problem in the convergence portion of the flash routine itself or perhaps a general stability problem with the equation of state. 

The bubble-point calculations, the dew-point calculations and the flash calculations tu-e not carried out in practice for any set of P, T, jr, and JC, . Rather, a subset of conditions which allow certain simplifications are selected and thermodynamic calculations are carried out They are ... 

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